Quick answer
Guilt invents pursuers. The verse contrasts a man running from nothing with one who has no reason to run.
Read both lines
The first line is a psychological observation and a precise one: there is no pursuer, and he flees anyway, which locates the problem entirely inside him. What the wicked man is fleeing is his own knowledge of what he has done, and the verse does not need to say so because the picture already has.
The second line answers with a lion, and the Hebrew word behind "bold" is the ordinary verb for trusting or being confident. So the righteous man is not brave in the sense of overcoming fear; he simply has nothing chasing him. That is the contrast the verse is drawing, and it is about the absence of a certain kind of interior noise rather than about temperament. A person with nothing to conceal moves differently, and everyone can see it.
Related: Proverbs 28:13 · Proverbs 10:9 · Proverbs 14:26 · Leviticus 26:17
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.